Answer
Minimum f(x,y)=x+y subject to the constrain g(x,y)=xy-16 is 8
Work Step by Step
f(x,y)=x+y
g(x,y)=xy-16
f(x,y)=λg(x,y)
i+j=λ(yi+xj)
∴ y=1/λ and x=1/λ
We know,
g(x,y)=0
xy-16=0
(1/λ)*(1/λ)=16
∴ λ=±1/4
∴x==±4 and y=±4
but given that x>0 and y>0
∴x=4 and y=4
∴f(4,4)=4+4=8.
